Notebook: Modélisation GAMMs des diphtongues descendantes (/ai/, /au/, /ei/, /ou/) en mandarin standard
Chenyu LI
2022-02-22
This notebook is for the acoustic analysis of the falling diphthongs in the standard Mandarin with the approach GAMMs.
#install.packages('rmarkdown')# Importation des emballages
#install.packages("itsadug")
library(ggplot2)
library(mgcv)## Loading required package: nlme## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.library(itsadug)## Loading required package: plotfunctions##
## Attaching package: 'plotfunctions'## The following object is masked from 'package:ggplot2':
##
## alpha## Loaded package itsadug 2.4 (see 'help("itsadug")' ).source("gamm_hacks.r")
#install.packages("tidyverse")
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✓ tibble 3.1.0 ✓ dplyr 1.0.5
## ✓ tidyr 1.1.3 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.1
## ✓ purrr 0.3.4## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x plotfunctions::alpha() masks ggplot2::alpha()
## x dplyr::collapse() masks nlme::collapse()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()After the importation of the packages, let’s read the data.
# Importation des données
au <- read.table(file="au0b.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ai <- read.table(file="ai0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ei <- read.table(file="ei0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ou <- read.table(file="ou0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)Change of the nature of the variables in the dataset.
The criterion is that all the numerical variables are numerated and the string varibles are factored.
1 /ai/
Lets start from /ai/:
ai$sexe<-as.factor(ai$sexe)
ai$ton<-as.factor(ai$ton)
ai$pow<-as.factor(ai$pow)
ai$contexte.D<-as.factor(ai$contexte.D)
ai$contexte.G<-as.factor(ai$contexte.G)
ai$f1<-as.numeric(ai$f1)## Warning: NAs introduced by coercionai$f2<-as.numeric(ai$f2)## Warning: NAs introduced by coercionai$f3<-as.numeric(ai$f3)## Warning: NAs introduced by coercionai$f0<-as.numeric(ai$f0)## Warning: NAs introduced by coercionhead(ai)## numero sexe locuteur diphtongue ton pow contexte.G contexte.D duree.ms.
## 1 1 F FS11 ai 4 f h 0 102.6625
## 2 1 F FS11 ai 4 f h 0 102.6625
## 3 1 F FS11 ai 4 f h 0 102.6625
## 4 1 F FS11 ai 4 f h 0 102.6625
## 5 1 F FS11 ai 4 f h 0 102.6625
## 6 1 F FS11 ai 4 f h 0 102.6625
## measurement.no f1 f2 f3 f0
## 1 0 770.9403 1592.367 2791.365 242.7606
## 2 1 789.5770 1654.538 2661.433 232.8865
## 3 2 790.5264 1676.141 2643.341 228.2137
## 4 3 792.7979 1771.876 2587.896 224.4104
## 5 4 786.4961 1814.919 2436.698 219.7656
## 6 5 760.0966 1827.338 2542.548 214.1222In the dataset we can see the number of the data numero, the gender sexe, the speaker locuteur, the tone ton, the position in the word pow, the context before and after this diphthong contexte.G / contexte.D, the duration of the diphthongs duree.ms. and f0, f1, f2, f3 trajectories, each of them represented by 11 measurements taken at equal intervals (at 0%, 10%, 20%, . . . , 100%).
# Regroupement par les facteurs
ai.mas <- droplevels(subset(ai,sexe=="M"))
ai.fem <- droplevels(subset(ai,sexe=="F"))1.1 Masculin
1.1.1 F1
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(ai.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(ai.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then the first model with a basic smooth of tone 1 and difference smooths.
ai.mas$ton.ord <- as.ordered(ai.mas$ton)
contrasts(ai.mas$ton.ord) <- "contr.treatment"
ai.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 508.92 20.76 24.514 < 2e-16 ***
## ton.ord2 120.43 22.33 5.393 8.47e-08 ***
## ton.ord3 173.89 23.07 7.536 1.01e-13 ***
## ton.ord4 109.93 21.51 5.110 3.81e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.434 5.392 5.263 5.67e-05 ***
## s(measurement.no):ton.ord2 1.017 1.032 10.413 0.00111 **
## s(measurement.no):ton.ord3 1.001 1.002 4.728 0.02980 *
## s(measurement.no):ton.ord4 3.570 4.385 7.968 1.47e-06 ***Then the plots of predictions and difference smooth.
plot_smooth(ai.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 7.575758plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.323232 - 10.000000plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.929293
## 6.969697 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
ai.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 521.48 20.47 25.471 < 2e-16 ***
## ton.ord2 96.33 22.45 4.291 1.94e-05 ***
## ton.ord3 174.32 22.42 7.777 1.74e-14 ***
## ton.ord4 97.59 21.32 4.578 5.25e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.526 5.458 2.689 0.0153 *
## s(duree.ms.) 5.581 6.507 5.202 3.61e-05 ***
## ti(measurement.no,duree.ms.) 7.258 9.082 4.050 3.73e-05 ***
## s(measurement.no):ton.ord2 2.838 3.498 7.788 1.66e-05 ***
## s(measurement.no):ton.ord3 2.279 2.815 3.364 0.0173 *
## s(measurement.no):ton.ord4 4.009 4.879 6.286 1.52e-05 ***The plots with regard the durations.
plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ai.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 515.84 19.38 26.619 < 2e-16 ***
## ton.ord2 98.96 21.39 4.628 4.21e-06 ***
## ton.ord3 133.59 22.60 5.912 4.69e-09 ***
## ton.ord4 99.55 19.87 5.009 6.49e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.043 6.028 3.347 0.002781 **
## s(f0) 2.675 3.219 6.283 0.000272 ***
## ti(measurement.no,f0) 3.877 4.994 2.958 0.011798 *
## s(measurement.no):ton.ord2 3.114 3.839 7.162 2.42e-05 ***
## s(measurement.no):ton.ord3 2.262 2.803 6.325 0.000460 ***
## s(measurement.no):ton.ord4 4.213 5.118 8.474 < 2e-16 ***The plot of such model.
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
#ai.mas.gam.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
# s(f0, bs="cr") +
# ti(measurement.no, f0) +
# s(measurement.no, by=ton.ord, bs="cr") +
# s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
# data=ai.mas, method="fREML")We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
ai.central<-droplevels(subset(ai,measurement.no>=2))
ai.central<-droplevels(subset(ai.central,measurement.no<=8))
ai.central.mas <- droplevels(subset(ai.central,sexe=="M"))
ai.central.fem <- droplevels(subset(ai.central,sexe=="F"))ai.central.mas$ton.ord <- as.ordered(ai.central.mas$ton)
contrasts(ai.central.mas$ton.ord) <- "contr.treatment"
ai.central.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 472.08 19.51 24.201 < 2e-16 ***
## ton.ord2 171.54 20.96 8.184 1.28e-15 ***
## ton.ord3 225.45 21.68 10.399 < 2e-16 ***
## ton.ord4 187.63 20.19 9.292 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.404 2.924 9.433 1.01e-05 ***
## s(measurement.no):ton.ord2 1.002 1.004 0.147 0.7039
## s(measurement.no):ton.ord3 1.002 1.005 1.309 0.2530
## s(measurement.no):ton.ord4 2.529 3.067 2.551 0.0533 .plot_smooth(ai.central.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.848485 - 8.000000plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 3.030303
## 5.818182 - 8.000000ai.central.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 483.05 19.43 24.864 < 2e-16 ***
## ton.ord2 153.92 21.26 7.239 1.19e-12 ***
## ton.ord3 225.56 21.26 10.609 < 2e-16 ***
## ton.ord4 175.66 20.20 8.697 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.393 2.910 10.314 3.87e-06 ***
## s(duree.ms.) 4.484 4.852 4.597 0.000297 ***
## ti(measurement.no,duree.ms.) 1.236 1.431 5.669 0.006689 **
## s(measurement.no):ton.ord2 1.000 1.000 0.094 0.759550
## s(measurement.no):ton.ord3 1.000 1.001 1.487 0.223105
## s(measurement.no):ton.ord4 2.587 3.131 2.965 0.029587 *plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 480.55 18.43 26.068 < 2e-16 ***
## ton.ord2 159.40 20.21 7.886 1.3e-14 ***
## ton.ord3 182.35 21.24 8.583 < 2e-16 ***
## ton.ord4 178.19 18.85 9.455 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.449 2.975 7.785 5.8e-05 ***
## s(f0) 2.888 3.362 5.997 0.000297 ***
## ti(measurement.no,f0) 1.005 1.010 6.139 0.013357 *
## s(measurement.no):ton.ord2 1.000 1.000 0.233 0.629530
## s(measurement.no):ton.ord3 1.000 1.001 0.006 0.938828
## s(measurement.no):ton.ord4 2.698 3.256 2.878 0.031657 *plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.1.2 F2
Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.
ggplot(ai.mas, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(ai.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then we fit the same model with a basic smooth of tone 1 and difference smooths.
ai.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1808.78 25.76 70.213 < 2e-16 ***
## ton.ord2 -190.78 27.71 -6.885 9.73e-12 ***
## ton.ord3 -182.21 28.63 -6.364 2.89e-10 ***
## ton.ord4 -157.18 26.70 -5.887 5.22e-09 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.783 4.654 6.929 7.58e-06 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.783 0.376
## s(measurement.no):ton.ord3 1.001 1.001 0.225 0.635
## s(measurement.no):ton.ord4 1.004 1.008 0.360 0.550Now the plots of f2 with different tones.
plot_smooth(ai.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 10.000000plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.020202plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 5.252525 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
ai.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1826.36 25.30 72.182 < 2e-16 ***
## ton.ord2 -210.79 27.64 -7.627 5.22e-14 ***
## ton.ord3 -190.56 27.77 -6.861 1.15e-11 ***
## ton.ord4 -178.75 26.32 -6.793 1.81e-11 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.893 4.783 8.213 6.26e-07 ***
## s(duree.ms.) 3.903 4.707 5.118 0.000252 ***
## ti(measurement.no,duree.ms.) 2.869 4.012 12.552 < 2e-16 ***
## s(measurement.no):ton.ord2 1.001 1.002 1.332 0.248618
## s(measurement.no):ton.ord3 1.001 1.003 0.351 0.553691
## s(measurement.no):ton.ord4 1.001 1.003 0.038 0.847241The plots with regard the durations.
plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1809.15 24.68 73.316 < 2e-16 ***
## ton.ord2 -187.20 27.28 -6.862 1.21e-11 ***
## ton.ord3 -201.12 28.74 -6.999 4.80e-12 ***
## ton.ord4 -156.85 25.33 -6.191 8.79e-10 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.100 5.036 9.733 < 2e-16 ***
## s(f0) 5.833 6.673 5.023 2.82e-05 ***
## ti(measurement.no,f0) 2.307 2.805 2.708 0.0422 *
## s(measurement.no):ton.ord2 1.001 1.002 0.005 0.9472
## s(measurement.no):ton.ord3 1.001 1.001 0.034 0.8553
## s(measurement.no):ton.ord4 1.004 1.008 0.011 0.9373plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The central portion:
ai.central.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1797.78 28.10 63.974 < 2e-16 ***
## ton.ord2 -169.65 30.20 -5.618 2.77e-08 ***
## ton.ord3 -154.65 31.23 -4.952 9.20e-07 ***
## ton.ord4 -136.24 29.09 -4.683 3.38e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.005 1.011 7.229 0.00732 **
## s(measurement.no):ton.ord2 1.001 1.002 0.268 0.60543
## s(measurement.no):ton.ord3 1.001 1.002 0.035 0.85460
## s(measurement.no):ton.ord4 1.001 1.003 0.595 0.44147plot_smooth(ai.central.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 6.242424 - 8.000000plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.939394 - 7.454545ai.central.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1809.11 27.47 65.867 < 2e-16 ***
## ton.ord2 -178.42 29.78 -5.992 3.30e-09 ***
## ton.ord3 -158.81 30.29 -5.243 2.09e-07 ***
## ton.ord4 -152.09 28.53 -5.331 1.32e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.106 1.204 6.368 0.01168 *
## s(duree.ms.) 2.613 3.155 4.432 0.00315 **
## ti(measurement.no,duree.ms.) 3.274 4.240 7.847 2.48e-06 ***
## s(measurement.no):ton.ord2 1.001 1.002 1.433 0.23173
## s(measurement.no):ton.ord3 1.001 1.002 0.023 0.88142
## s(measurement.no):ton.ord4 1.002 1.003 0.342 0.56017plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1808.72 25.82 70.057 < 2e-16 ***
## ton.ord2 -183.71 28.33 -6.485 1.74e-10 ***
## ton.ord3 -198.13 29.76 -6.658 5.86e-11 ***
## ton.ord4 -147.99 26.51 -5.582 3.48e-08 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.001 1.002 9.506 0.00212 **
## s(f0) 4.105 4.579 7.115 2.97e-06 ***
## ti(measurement.no,f0) 5.049 5.936 5.348 2.37e-05 ***
## s(measurement.no):ton.ord2 1.001 1.001 0.421 0.51700
## s(measurement.no):ton.ord3 1.001 1.001 0.465 0.49561
## s(measurement.no):ton.ord4 1.001 1.001 0.610 0.43499plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2 Féminin
1.2.1 F1
We now switch to the data of feminin subjects. First we drow the trajectories of f1 in different tones with regard of the sexes and the durations with ggplot2.
ggplot(ai.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then the first model with a basic smooth of tone 1 and difference smooths.
ai.fem$ton.ord <- as.ordered(ai.fem$ton)
contrasts(ai.fem$ton.ord) <- "contr.treatment"
ai.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 727.300 10.502 69.251 < 2e-16 ***
## ton.ord2 41.824 12.745 3.282 0.00106 **
## ton.ord3 9.285 13.129 0.707 0.47957
## ton.ord4 -4.129 11.138 -0.371 0.71090
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.990 6.014 22.139 < 2e-16 ***
## s(measurement.no):ton.ord2 1.976 2.459 3.589 0.02225 *
## s(measurement.no):ton.ord3 1.004 1.008 4.710 0.03005 *
## s(measurement.no):ton.ord4 2.916 3.598 4.183 0.00373 **Then the plots of predictions and difference smooth.
plot_smooth(ai.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 4.343434plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.323232
## 7.777778 - 10.000000plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.828283
## 6.161616 - 7.676768The model that accounts for the influence of duree.ms. on the trajectories.
ai.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 725.48603 10.51394 69.002 < 2e-16 ***
## ton.ord2 38.51010 12.39140 3.108 0.00193 **
## ton.ord3 9.42465 13.15220 0.717 0.47377
## ton.ord4 0.02272 11.37780 0.002 0.99841
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.275 6.330 25.533 < 2e-16 ***
## s(duree.ms.) 7.132 8.041 6.159 < 2e-16 ***
## ti(measurement.no,duree.ms.) 8.571 10.747 5.436 < 2e-16 ***
## s(measurement.no):ton.ord2 2.039 2.534 3.642 0.01899 *
## s(measurement.no):ton.ord3 1.007 1.012 10.009 0.00158 **
## s(measurement.no):ton.ord4 2.434 3.015 2.159 0.09079 .The plots with regard the durations.
plot_smooth(ai.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ai.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 726.023 10.603 68.474 <2e-16 ***
## ton.ord2 36.953 14.222 2.598 0.0095 **
## ton.ord3 15.256 14.126 1.080 0.2804
## ton.ord4 -2.092 11.020 -0.190 0.8494
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.092 6.142 32.725 < 2e-16 ***
## s(f0) 1.000 1.000 1.679 0.195397
## ti(measurement.no,f0) 2.285 2.770 5.741 0.000985 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.466 0.495028
## s(measurement.no):ton.ord3 1.000 1.001 0.245 0.620400
## s(measurement.no):ton.ord4 2.564 3.184 3.425 0.015002 *The plot of such model.
plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
#ai.mas.gam.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
# s(f0, bs="cr") +
# ti(measurement.no, f0) +
# s(measurement.no, by=ton.ord, bs="cr") +
# s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
# data=ai.mas, method="fREML")We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
ai.central.fem$ton.ord <- as.ordered(ai.central.fem$ton)
contrasts(ai.central.fem$ton.ord) <- "contr.treatment"
ai.central.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 764.464 10.337 73.951 <2e-16 ***
## ton.ord2 23.456 12.626 1.858 0.0636 .
## ton.ord3 1.278 13.036 0.098 0.9219
## ton.ord4 6.941 10.981 0.632 0.5275
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.787 3.350 9.759 1.85e-06 ***
## s(measurement.no):ton.ord2 1.002 1.005 3.192 0.0744 .
## s(measurement.no):ton.ord3 1.002 1.005 5.494 0.0192 *
## s(measurement.no):ton.ord4 2.339 2.843 2.021 0.1193plot_smooth(ai.central.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 4.848485plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.787879 - 7.090909plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 2.969697
## 5.151515 - 8.000000ai.central.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 765.093 10.573 72.362 <2e-16 ***
## ton.ord2 24.013 12.492 1.922 0.055 .
## ton.ord3 -2.690 13.290 -0.202 0.840
## ton.ord4 6.656 11.439 0.582 0.561
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.800 3.363 10.238 9.86e-07 ***
## s(duree.ms.) 4.244 4.713 3.477 0.0354 *
## ti(measurement.no,duree.ms.) 2.227 2.802 2.612 0.0375 *
## s(measurement.no):ton.ord2 1.001 1.002 3.054 0.0809 .
## s(measurement.no):ton.ord3 1.001 1.002 5.522 0.0190 *
## s(measurement.no):ton.ord4 2.354 2.860 2.097 0.1080plot_smooth(ai.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 753.01 10.66 70.639 <2e-16 ***
## ton.ord2 40.34 14.26 2.829 0.0048 **
## ton.ord3 25.36 14.31 1.771 0.0769 .
## ton.ord4 14.76 11.07 1.333 0.1828
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.956 3.535 12.622 < 2e-16 ***
## s(f0) 1.000 1.001 9.090 0.00265 **
## ti(measurement.no,f0) 1.003 1.006 7.019 0.00817 **
## s(measurement.no):ton.ord2 1.001 1.002 1.025 0.31201
## s(measurement.no):ton.ord3 1.001 1.001 1.560 0.21208
## s(measurement.no):ton.ord4 2.117 2.590 1.603 0.18325plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2.2 F2
Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.
ggplot(ai.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
ggplot(ai.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then we fit the same model with a basic smooth of tone 1 and difference smooths.
ai.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2038.36 17.15 118.880 < 2e-16 ***
## ton.ord2 -107.98 20.81 -5.189 2.49e-07 ***
## ton.ord3 -88.98 21.43 -4.152 3.53e-05 ***
## ton.ord4 -70.79 18.18 -3.893 0.000105 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.280 5.234 3.945 0.001255 **
## s(measurement.no):ton.ord2 1.002 1.005 22.811 2.65e-06 ***
## s(measurement.no):ton.ord3 2.149 2.673 9.920 9.98e-06 ***
## s(measurement.no):ton.ord4 1.003 1.005 11.113 0.000866 ***Now the plots of f2 with different tones.
plot_smooth(ai.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 6.666667plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.545455 - 5.959596plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.424242The model that accounts for the influence of duree.ms. on the trajectories.
ai.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2038.81 17.36 117.410 < 2e-16 ***
## ton.ord2 -102.76 20.46 -5.023 5.88e-07 ***
## ton.ord3 -87.08 21.69 -4.014 6.35e-05 ***
## ton.ord4 -73.67 18.78 -3.922 9.29e-05 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.356 5.321 4.858 0.000157 ***
## s(duree.ms.) 6.537 7.514 5.600 1.96e-06 ***
## ti(measurement.no,duree.ms.) 3.189 3.659 7.475 1.13e-05 ***
## s(measurement.no):ton.ord2 1.002 1.005 21.541 3.84e-06 ***
## s(measurement.no):ton.ord3 2.182 2.713 8.207 6.17e-05 ***
## s(measurement.no):ton.ord4 1.004 1.007 4.444 0.034836 *The plots with regard the durations.
plot_smooth(ai.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2006.20 17.59 114.025 <2e-16 ***
## ton.ord2 -47.56 23.69 -2.008 0.0449 *
## ton.ord3 -39.15 23.59 -1.660 0.0972 .
## ton.ord4 -33.95 18.66 -1.819 0.0691 .
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.765 4.647 3.339 0.006051 **
## s(f0) 4.465 5.325 9.702 < 2e-16 ***
## ti(measurement.no,f0) 1.001 1.002 3.953 0.046912 *
## s(measurement.no):ton.ord2 1.000 1.001 7.075 0.007921 **
## s(measurement.no):ton.ord3 1.878 2.345 4.999 0.004516 **
## s(measurement.no):ton.ord4 1.001 1.002 14.369 0.000158 ***plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The central portion:
ai.central.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2048.03 17.96 114.046 < 2e-16 ***
## ton.ord2 -110.36 21.93 -5.032 6.06e-07 ***
## ton.ord3 -68.99 22.65 -3.047 0.00239 **
## ton.ord4 -74.75 19.08 -3.919 9.70e-05 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.354 1.610 3.247 0.03218 *
## s(measurement.no):ton.ord2 1.002 1.003 7.512 0.00623 **
## s(measurement.no):ton.ord3 1.002 1.004 6.353 0.01188 *
## s(measurement.no):ton.ord4 1.108 1.194 1.388 0.20091plot_smooth(ai.central.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 6.727273plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.757576 - 5.818182plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 5.333333ai.central.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2057.82 18.18 113.168 < 2e-16 ***
## ton.ord2 -114.28 21.48 -5.321 1.36e-07 ***
## ton.ord3 -74.34 22.87 -3.251 0.0012 **
## ton.ord4 -88.36 19.67 -4.491 8.18e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.226 1.395 6.156 0.005088 **
## s(duree.ms.) 4.351 4.781 5.615 0.000994 ***
## ti(measurement.no,duree.ms.) 2.317 2.905 5.698 0.001249 **
## s(measurement.no):ton.ord2 1.001 1.002 7.310 0.006986 **
## s(measurement.no):ton.ord3 1.001 1.002 4.581 0.032602 *
## s(measurement.no):ton.ord4 1.276 1.479 0.171 0.687964plot_smooth(ai.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2010.59 18.67 107.680 <2e-16 ***
## ton.ord2 -46.55 25.44 -1.830 0.0677 .
## ton.ord3 -24.49 25.01 -0.979 0.3278
## ton.ord4 -31.78 19.74 -1.610 0.1079
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.019 1.036 9.108 0.00263 **
## s(f0) 3.656 4.215 12.066 < 2e-16 ***
## ti(measurement.no,f0) 2.960 3.539 4.413 0.00284 **
## s(measurement.no):ton.ord2 1.001 1.001 2.724 0.09917 .
## s(measurement.no):ton.ord3 1.001 1.001 2.309 0.12896
## s(measurement.no):ton.ord4 1.158 1.296 1.005 0.41341plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2 /au/
The next diphthong we look at is /au/.
au$sexe<-as.factor(au$sexe)
au$ton<-as.factor(au$ton)
au$pow<-as.factor(au$pow)
au$contexte.D<-as.factor(au$contexte.D)
au$contexte.G<-as.factor(au$contexte.G)
au$f1<-as.numeric(au$f1)## Warning: NAs introduced by coercionau$f2<-as.numeric(au$f2)## Warning: NAs introduced by coercionau$f3<-as.numeric(au$f3)## Warning: NAs introduced by coercionau$f0<-as.numeric(au$f0)## Warning: NAs introduced by coercion# Regroupement par les facteurs
au.mas <- droplevels(subset(au,sexe=="M"))
au.fem <- droplevels(subset(au,sexe=="F"))2.1 Masculin
2.1.1 F1
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(au.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(au.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
Then the first model with a basic smooth of tone 1 and difference smooths.
au.mas$ton.ord <- as.ordered(au.mas$ton)
contrasts(ai.mas$ton.ord) <- "contr.treatment"
au.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 653.579 6.079 107.522 < 2e-16 ***
## ton.ord.L 92.904 10.611 8.755 < 2e-16 ***
## ton.ord.Q -79.485 12.157 -6.538 9.4e-11 ***
## ton.ord.C 43.908 13.528 3.246 0.00121 **
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.228 6.297 17.678 < 2e-16 ***
## s(measurement.no):ton.ord2 1.133 1.254 2.295 0.09241 .
## s(measurement.no):ton.ord3 1.002 1.005 0.364 0.54665
## s(measurement.no):ton.ord4 1.016 1.032 8.584 0.00342 **Then the plots of predictions and difference smooth.
plot_smooth(au.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 10.000000plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.525253
## 6.868687 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
au.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 650.142 6.024 107.929 < 2e-16 ***
## ton.ord.L 98.438 10.450 9.420 < 2e-16 ***
## ton.ord.Q -72.959 12.090 -6.035 2.16e-09 ***
## ton.ord.C 42.837 13.539 3.164 0.0016 **
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.099 6.148 9.388 < 2e-16 ***
## s(duree.ms.) 6.844 7.743 5.934 4.75e-07 ***
## ti(measurement.no,duree.ms.) 5.769 7.821 2.188 0.03051 *
## s(measurement.no):ton.ord2 1.228 1.417 1.818 0.11762
## s(measurement.no):ton.ord3 1.003 1.005 0.390 0.53369
## s(measurement.no):ton.ord4 2.064 2.565 4.619 0.00881 **The plots with regard the durations.
plot_smooth(au.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
au.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 646.170 5.867 110.142 < 2e-16 ***
## ton.ord.L 66.939 11.132 6.013 2.63e-09 ***
## ton.ord.Q -73.220 12.391 -5.909 4.86e-09 ***
## ton.ord.C 56.950 13.067 4.358 1.46e-05 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.303 6.384 17.712 < 2e-16 ***
## s(f0) 6.430 7.259 11.991 < 2e-16 ***
## ti(measurement.no,f0) 1.001 1.001 19.887 9.23e-06 ***
## s(measurement.no):ton.ord2 1.987 2.477 1.399 0.222
## s(measurement.no):ton.ord3 1.001 1.002 1.609 0.205
## s(measurement.no):ton.ord4 1.001 1.002 0.023 0.882The plot of such model.
plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
au.central<-droplevels(subset(au,measurement.no>=2))
au.central<-droplevels(subset(au.central,measurement.no<=8))
au.central.mas <- droplevels(subset(au.central,sexe=="M"))
au.central.fem <- droplevels(subset(au.central,sexe=="F"))au.central.mas$ton.ord <- as.ordered(au.central.mas$ton)
contrasts(au.central.mas$ton.ord) <- "contr.treatment"
au.central.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 558.70 13.33 41.901 < 2e-16 ***
## ton.ord2 153.73 22.20 6.926 9.46e-12 ***
## ton.ord3 148.03 15.44 9.588 < 2e-16 ***
## ton.ord4 153.02 14.19 10.781 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.692 3.266 9.376 2.94e-06 ***
## s(measurement.no):ton.ord2 1.003 1.007 2.218 0.1358
## s(measurement.no):ton.ord3 1.001 1.002 2.129 0.1449
## s(measurement.no):ton.ord4 1.000 1.001 5.466 0.0197 *plot_smooth(au.central.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.au.central.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 553.39 12.75 43.405 < 2e-16 ***
## ton.ord2 149.36 21.42 6.971 7.04e-12 ***
## ton.ord3 144.26 14.73 9.790 < 2e-16 ***
## ton.ord4 163.53 13.64 11.987 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.768 3.350 9.836 1.6e-06 ***
## s(duree.ms.) 4.797 4.975 12.714 < 2e-16 ***
## ti(measurement.no,duree.ms.) 1.342 1.603 7.822 0.00402 **
## s(measurement.no):ton.ord2 1.002 1.003 3.412 0.06477 .
## s(measurement.no):ton.ord3 1.001 1.001 2.348 0.12578
## s(measurement.no):ton.ord4 1.002 1.004 4.081 0.04380 *plot_smooth(au.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 567.54 13.32 42.604 < 2e-16 ***
## ton.ord2 144.91 21.04 6.886 1.44e-11 ***
## ton.ord3 110.99 16.53 6.716 4.32e-11 ***
## ton.ord4 126.86 14.31 8.869 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.753 3.334 6.987 8.87e-05 ***
## s(f0) 4.636 4.908 12.260 < 2e-16 ***
## ti(measurement.no,f0) 1.526 1.880 6.984 0.00104 **
## s(measurement.no):ton.ord2 1.104 1.199 0.634 0.52311
## s(measurement.no):ton.ord3 1.001 1.001 0.104 0.74696
## s(measurement.no):ton.ord4 1.000 1.001 0.516 0.47274plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.1.2 F2
Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.
ggplot(au.mas, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(au.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
au.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1146.0817 16.3782 69.976 < 2e-16 ***
## ton.ord.L 90.9336 28.5895 3.181 0.00151 **
## ton.ord.Q 43.3800 32.7569 1.324 0.18567
## ton.ord.C -0.6071 36.4515 -0.017 0.98672
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.666 5.675 18.874 <2e-16 ***
## s(measurement.no):ton.ord2 1.784 2.221 0.541 0.526
## s(measurement.no):ton.ord3 1.005 1.011 1.026 0.309
## s(measurement.no):ton.ord4 1.003 1.006 0.830 0.362Now the plots of f2 with different tones.
plot_smooth(au.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.737374 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
au.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1144.7951 16.5584 69.137 < 2e-16 ***
## ton.ord.L 92.7316 28.8176 3.218 0.00133 **
## ton.ord.Q 44.8780 32.9935 1.360 0.17403
## ton.ord.C -0.9374 36.4501 -0.026 0.97949
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.674 5.685 19.246 <2e-16 ***
## s(duree.ms.) 1.002 1.003 0.149 0.700
## ti(measurement.no,duree.ms.) 4.177 5.924 0.988 0.403
## s(measurement.no):ton.ord2 1.491 1.827 0.365 0.696
## s(measurement.no):ton.ord3 1.017 1.033 0.971 0.315
## s(measurement.no):ton.ord4 1.002 1.004 0.825 0.363The plots with regard the durations.
plot_smooth(au.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1145.1726 16.3532 70.028 < 2e-16 ***
## ton.ord.L 79.9037 30.4263 2.626 0.00878 **
## ton.ord.Q 30.5677 34.3775 0.889 0.37414
## ton.ord.C 0.3648 36.1553 0.010 0.99195
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.420 5.403 16.115 < 2e-16 ***
## s(f0) 1.000 1.000 0.022 0.88388
## ti(measurement.no,f0) 1.001 1.002 8.948 0.00285 **
## s(measurement.no):ton.ord2 2.161 2.690 1.530 0.28340
## s(measurement.no):ton.ord3 1.001 1.002 2.489 0.11474
## s(measurement.no):ton.ord4 1.001 1.002 0.204 0.65200plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The central portion:
au.central.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1021.70 38.86 26.290 <2e-16 ***
## ton.ord2 -41.61 64.69 -0.643 0.5203
## ton.ord3 70.25 45.00 1.561 0.1189
## ton.ord4 137.90 41.37 3.334 0.0009 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.745 2.121 1.417 0.2323
## s(measurement.no):ton.ord2 1.001 1.002 0.020 0.8896
## s(measurement.no):ton.ord3 1.002 1.005 0.757 0.3836
## s(measurement.no):ton.ord4 1.893 2.307 2.377 0.0804 .plot_smooth(au.central.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.969697 - 7.272727plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 6.000000 - 8.000000plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.060606 - 8.000000au.central.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1023.68 38.89 26.324 < 2e-16 ***
## ton.ord2 -40.19 64.86 -0.620 0.53563
## ton.ord3 69.89 44.92 1.556 0.12012
## ton.ord4 134.96 41.55 3.248 0.00121 **plot_smooth(au.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1011.64 37.07 27.290 < 2e-16 ***
## ton.ord2 -29.61 58.83 -0.503 0.614896
## ton.ord3 88.26 45.33 1.947 0.052013 .
## ton.ord4 138.85 39.62 3.505 0.000491 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.119 1.210 0.434 0.4770
## s(f0) 1.000 1.000 0.357 0.5506
## ti(measurement.no,f0) 1.002 1.004 1.509 0.2199
## s(measurement.no):ton.ord2 1.000 1.000 0.206 0.6501
## s(measurement.no):ton.ord3 1.001 1.001 0.490 0.4838
## s(measurement.no):ton.ord4 2.243 2.742 3.078 0.0267 *plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
3 /ei/
The third one is diphthong /ei/.
ei$sexe<-as.factor(ei$sexe)
ei$ton<-as.factor(ei$ton)
ei$pow<-as.factor(ei$pow)
ei$contexte.D<-as.factor(ei$contexte.D)
ei$contexte.G<-as.factor(ei$contexte.G)
ei$f1<-as.numeric(ei$f1)## Warning: NAs introduced by coercionei$f2<-as.numeric(ei$f2)## Warning: NAs introduced by coercionei$f3<-as.numeric(ei$f3)## Warning: NAs introduced by coercionei$f0<-as.numeric(ei$f0)## Warning: NAs introduced by coercion# Regroupement par les facteurs
ei.mas <- droplevels(subset(ei,sexe=="M"))
ei.fem <- droplevels(subset(ei,sexe=="F"))3.1 Masculin
3.1.1 F1
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(ei.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 17 row(s) containing missing values (geom_path).
ggplot(ei.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
The basic model with the tone.
ei.mas$ton.ord <- as.ordered(ei.mas$ton)
contrasts(ei.mas$ton.ord) <- "contr.treatment"
ei.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 382.24 21.92 17.440 < 2e-16 ***
## ton.ord2 15.28 26.52 0.576 0.564521
## ton.ord3 80.97 23.54 3.439 0.000604 ***
## ton.ord4 96.06 24.49 3.922 9.27e-05 ***Then the plots of predictions and difference smooth.
plot_smooth(ei.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.505051 - 8.181818plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.The model that accounts for the influence of duree.ms. on the trajectories.
ei.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 383.014 22.572 16.969 < 2e-16 ***
## ton.ord2 2.031 27.687 0.073 0.941525
## ton.ord3 90.245 24.282 3.717 0.000211 ***
## ton.ord4 85.518 25.448 3.361 0.000803 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.006 1.011 0.711 0.3988
## s(duree.ms.) 7.575 8.320 8.362 <2e-16 ***
## ti(measurement.no,duree.ms.) 5.104 6.914 2.222 0.0305 *
## s(measurement.no):ton.ord2 2.143 2.663 0.964 0.3046
## s(measurement.no):ton.ord3 1.471 1.798 0.207 0.7371
## s(measurement.no):ton.ord4 1.005 1.010 1.189 0.2746The plots with regard the durations.
plot_smooth(ei.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ei.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 69.653645 to 160.541647.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ei.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 399.41 22.83 17.494 < 2e-16 ***
## ton.ord2 17.73 27.32 0.649 0.516427
## ton.ord3 51.91 25.31 2.051 0.040519 *
## ton.ord4 97.15 25.32 3.837 0.000131 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.002 1.003 1.014 0.3142
## s(f0) 5.427 6.335 7.715 <2e-16 ***
## ti(measurement.no,f0) 2.687 3.138 2.545 0.0699 .
## s(measurement.no):ton.ord2 2.055 2.568 1.245 0.2285
## s(measurement.no):ton.ord3 1.003 1.006 0.006 0.9567
## s(measurement.no):ton.ord4 1.002 1.003 2.035 0.1536The plot of such model.
plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ei.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 92.830073 to 209.388440.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ei.mas.gam.f0.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.f0.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 391.24 23.22 16.853 < 2e-16 ***
## ton.ord2 15.12 28.39 0.532 0.594501
## ton.ord3 70.49 25.83 2.729 0.006447 **
## ton.ord4 96.54 26.13 3.695 0.000231 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.002 1.004 2.001 0.1573
## s(f0) 5.595 6.509 7.350 <2e-16 ***
## ti(measurement.no,f0) 2.900 3.338 3.492 0.0267 *
## s(duree.ms.) 7.761 8.457 9.119 <2e-16 ***
## ti(measurement.no,duree.ms.) 5.515 7.444 1.983 0.0539 .
## s(measurement.no):ton.ord2 2.300 2.862 2.052 0.0837 .
## s(measurement.no):ton.ord3 1.003 1.006 0.099 0.7580
## s(measurement.no):ton.ord4 1.002 1.003 1.069 0.3013plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.f0.dur, view=c("measurement.no","f0"),
ylim=quantile(ei.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 92.830073 to 209.388440.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
4 Analysis
4.1 Factor duration
The influence of the factor duration is commun in all the diphthongs. All the diphthongs will be realized as more monophthongized with a brief duration.
4.2 Factor f0
The General influence of the factor of f0 on the f1 and f2 is as such:
f0 and f1 is a negative correlation.
f0 and f2 is a positive correlation.
However, this correlation is influenced by other factors and not on the same level within the different diphthongs.
In diphthong /ai/, the correlation between f0 and f1 is positive within the female data, which should be regarded after.